Can neural networks be better than human experts at prediction of greyhound racing results?
Practically, no. 


In greyhound racing (or horse racing), there is no definite underlying pattern that can be associated with the outcome of the race. There are far too many variables to record and code as features. Most of which cannot be accessed by the public. This includes eating, sleeping, and training patterns. Furthermore, there are variables that cannot be readily quantified, such as the trainer's techniques, training effort, health history, and genes. A mere history of racing results and age won't be that helpful. 

A neural network can only be as good as the features that are used to represent the instances. If the features don't capture the necessary characteristics of the instances that are associated with the problem, then the learner cannot generalize to predict the real world outcome.